The Sparsity and Incoherence in Compressive Sensing as Applied to Field Reconstruction

Compressed Sensing Vs. Auto-Encoder: On the Perspective of Signal Compression and Restoration

“…CS expresses the original signal with a reduced number of measurements and restores the signal through a recovery algorithm. Two conditions must be met for successful signal recovery [6]:…”

“…RIP also affects OMP. In condition (6), If (K +1, δ)-RIP and δ ≤ 1 3 √ K , OMP can restore the K -sparse vector in K iteration [30], [55]. Similarly, in the case of CoSaMP, if (cK , δ)-RIP, where the c is a parameter of RIP, x can be restored from y.…”

Accurate Reconstruction of the Radiation of Sparse Sources from a Small Set of Near-Field Measurements by Means of a Smooth-Weighted Norm for Cluster-Sparsity Problems

“…In Figure 7, we can see the comparison of cumulative density function of the reconstruction error (17) for the standard algorithm and the proposed algorithm, ran with the same noise realization (with a SNR of 40 dB): the "smooth" algorithm shows a much smaller reconstruction error on the far-field.…”

“…In particular, many of these approaches have been inspired, by the compressive sensing paradigm [7], that exploits the knowledge of the sparsity of the chosen representation of the source to reduce the number of needed measurements. Some of these approaches have been aimed to the estimation of the far-field pattern from a limited number of points [8][9][10][11][12][13][14][15][16][17]; other methods have been developed for the identification of the failures of the radiating elements of arrays [18][19][20][21][22]. A review of the NF measurement techniques is reported in [23].…”